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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On the group of homotopy equivalences
of a manifold


Author: Hans Joachim Baues
Journal: Trans. Amer. Math. Soc. 348 (1996), 4737-4773
MSC (1991): Primary 55O10, 57O50
MathSciNet review: 1340168
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Abstract: We consider the group of homotopy equivalences $\mathcal E(M)$ of a simply connected manifold $M$ which is part of the fundamental extension of groups due to Barcus-Barratt. We show that the kernel of this extension is always a finite group and we compute this kernel for various examples. This leads to computations of the group $\mathcal E(M)$ for special manifolds $M$, for example if $M$ is a connected sum of products $S^n\times S^m$ of spheres. In particular the group $\mathcal E(S^n\times S^n)$ is determined completely. Also the connection of $\mathcal E(M)$ with the group of isotopy classes of diffeomorphisms of $M$ is studied.


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Additional Information

Hans Joachim Baues
Affiliation: Max Planck Institute for Mathematics, Gottfried-Claren-Strasse 26, 53225 Bonn, Germany
Email: baues@mpim-bonn.mpg.de

DOI: https://doi.org/10.1090/S0002-9947-96-01555-3
Received by editor(s): August 17, 1994
Article copyright: © Copyright 1996 American Mathematical Society